Experimental analysis on waterjet-guided Nd: YAG laser thin wood machining

Waterjet-Guided Laser (WJGL) machining is an advanced technique providing efficiency and precision for wood machining. The present study investigates the practical demonstration and analysis of laminated object manufacturing (LOM) WJGL for thin wood machining. A theoretical process of wood laser cutting was established, expressing relations between the cut kerf width and the influencing parameters. WJG Nd: YAG laser system was utilized for machining Korean pine and Northeast China ash specimen of 3 mm thickness, each with 7.21 and 7.13% of water content, respectively, under different machining conditions. The effects of process parameters and influences on woodcut surface geometry were analyzed via analysis of variance (ANOVA) and scanning electron microscopy (SEM). The investigated parameters include the laser cutting speed, power, kerf width, heat-affected zone (HAZ), and cut surface roughness. The study shows that the kerf width and surface were significantly influenced by WJGL power, followed by the cutting speed. For both wood specimens, at a fixed laser cutting speed of 2.36 mm/s, the kerf width increases significantly with laser power, affecting the cut surface quality accordingly. At 6 W and 8 W, the cut kerf geometry and surface quality were excellent for the Pinus Koraiensis, with kerf widths of 0.79 and 0.852 mm, respectively. At a fixed laser power of 8 W, the kerf width decreases with the cutting speed, affecting the cut surface quality. At a cutting speed of 4.33 mm/s, an excellent cut surface of Fraxinus mandshurica was observed with 0.808 mm of kerf width. Depending on the machining conditions, the kerf width variations of Korean pine were more significant than the Northeast China ash. LOM-WJGL is an efficient and eco-friendly technique for thin wood processing. Practical modeling demonstration of waterjet guided laser (WJGL) wood machining. Experimental investigation of different wood specimens under influenced process parameters and machining conditions. Characterization and identification of suitable wood types for efficient and eco-friendly applications. Practical modeling demonstration of waterjet guided laser (WJGL) wood machining. Experimental investigation of different wood specimens under influenced process parameters and machining conditions. Characterization and identification of suitable wood types for efficient and eco-friendly applications.


Introduction
The recent growth of Advanced Manufacturing (AM) techniques using hybrid processes makes lasers vital, making things more straightforward and comfortable. In laminated object manufacturing (LOM), laser cutting is an applied technique with numerous lasers. The overwhelmingly used ones are conventional lasers such as carbon dioxide (CO 2 ), fiber/disk, neodymium-doped: yttrium-aluminum-garnet (Nd: YAG), and direct diode lasers [1][2][3]. The selection among these competing laser cutting systems depends mainly on the proceeded material, the efficiency (cut quality, small heat-affected zone), the flexibility of cutting regarding laser output power and cutting speed, and the process's ability to automatize [4,5]. However, in terms of cutting objects, CO 2 and Nd: YAG lasers and derivatives are overwhelmingly used for machining a wide range of materials. They react differently with materials depending on their wavelength. The CO 2 laser is roughly 10.64 µm of wavelength, whereas the Nd: YAG laser is 1.064 µm of wavelength, which is readably ten times smaller than the CO 2 laser. Most nonmetallic materials (organic materials), including wood, are highly absorbent at the 10.6 µm wavelength of the CO 2 laser [6][7][8]. Whereas most metallic materials mainly absorb the short wavelength of YAG laser, it cripples its ability to absorb many other materials, including wood, acrylic, plastics, and fabrics. As a result, the Nd: YAG laser is one of the most widely used high-power solid-state lasers for high precision and micro-processing applications worldwide due to its theoretical focal point diameter [9,10]. Consequently, its application for nonmetallic materials processing has seen considerable growth.
The pulse duration and pause duration alternate at short intervals in pulsed mode, and the laser provides pulses with high output [5,11]. In addition, shortening the pulse width of lasers allows the surrounding area heat effects to be controlled while increasing the peak power [12]. This mode is suited for materials processing, namely, cutting, welding, and hole drilling [7,13]. Lowpowered lasers mainly use this process, resulting in a narrow, clean kerf width. Pulsed lasers are flexible systems having achieved numerous functions in optical physics. They have received special consideration in studying transient phenomena which occur in periods [14]. Overwhelmingly applied for decades to various materials, pulsed lasers have become prominent in AM technologies [5,15]. Indeed since the 1970s, the laser has been used for wood processing as dies in the packaging industry [16]. The current application of pulsed lasers covers different types of wood materials for multiple uses, including furniture, car interiors, architecture, and indoor and outdoor decoration [5,[16][17][18].
In terms of thin wood laminated wooden parts machining, a certain number of studies have investigated the use of pulsed Nd: YAG solid-state lasers. Yang et al. proposed the nanosecond laser processing theory of micronized wood fibers and demonstrated the possibility of microthin wood fibers machining along the grain [19]. Jiang et al. used a pulsed Nd: YAG laser to cut 2 mm thick of different types of wood and study the impact of laser energy, feed rate, and kerf depth on the cut surface quality [20]. This study found significant kerf width dependency on laser pulse frequency and power. According to wood types, the increase of laser power reduced the molten slag on the wood kerf surface, improving its smoothness and quality. Bakary et al. currently analyzed the theoretical and practical use prospects of the pulsed Nd: YAG laser for wood veneers micromachining and found it not only eco-friendly but safe, versatile, and fast technique with less restriction resulting in a smooth cut surface with narrow kerf width without significant thermal deformation [5]. However, this study was limited to a process free of burrs and burns on the cut surface.
On the other hand, laser process efficiency in terms of versatility, eco-friendness, production capability, and in some cases, the nozzle selection and energy carriage, gas/or water-assisted laser leads to outstanding machining results [3,5,[20][21][22][23]. Thus, WJGL is a new innovative technique that uses different laser sources assisted by waterjet for machining objects. Using the Nd: YAG laser source, WJGL technology provides high-precision operations without blurs with less heat and free debris on the cutting surface compared to conventional techniques [24]. Recently, Chunmei et al. have used Nd: YAG laser and waterjet guiding systems for wood laser processing to introduce a new CNC test bench for hybrid WJG Nd: YAG laser wood processing [22]. This hybrid WJGL technique is similar to the one proposed by Tangwarodomnukun et al. [25]. The process exploits the advantages of laser processing assisted off-axially by waterjet to expel debris while cooling the processed area for near thermal damage-free micromachining. Since the waterjet runs offaxially with the laser beam during processing, the distance between the two nozzles, the angle, and the waterjet offset distance, are controlled to minimize the laser beam and waterjet overlap limiting water absorption laser energy and therefore reducing heat loss. Nonetheless, heat loss at the irradiated surface may occur when the laser beam interacts with a thin water layer. The higher the power density of the laser beam energy, the greater the absorption in the water, limiting the processing efficiency of the WJGL system resulting in the slow cutting of materials [24]. As a result, different studies have been carried out using the waterjet-assisted pulsed Nd: YAG laser to cut wood parts [26,27]. These studies analyzed the cut surface quality under the effects of process parameters and gave merit to this hybrid WJGL technique compared to conventional Nd: YAG laser cutting in terms of machining quality and efficiency.
However, considering the benefits of laser processing and, in particular, the pulsed Nd: YAG laser micromachining, plus the merit given to WJG Nd: YAG laser wood machining, there is a lack of investigations comparing the machining quality under the same conditions of different types of wood. Besides, there is no practical investigation considering the theoretical and feasibility analysis of using WJG pulsed Nd: YAG laser for wood micromachining. Therefore, besides theoretically describing the feasibility prospects, this study practically investigates using a hybrid WJG pulsed Nd: YAG laser for different thin wood micromachining under the same machining conditions. Among the two main groups of wood materials, namely, hardwood and softwood, Ash and Red pine types are selected for workpieces. These wood materials characterize hybrid WJG Nd: YAG laser thin wood micromachining. This manuscript is divided into five sections, outlined as follows. Next, we consider a theoretical analysis of laser cutting, the WJGL process, and the hybrid WJGL wood micromachining process. Section 3 shows the experimental feasibilities. In Sect. 4, the experimental findings are presented and analyzed, followed by a brief conclusion.

Laser cutting process
A laser cutting is a thermal process involving heating a specific workpiece material with a focused laser beam [16]. The process forms a cut kerf on the workpiece while burning or vaporizing throughout the material thickness, assisted with pressurized gas or waterjet acting co-axially to blow away the debris [7,28]. It is a famous process used in most manufacturing industries to cut metallic and nonmetallic materials [29]. Nowadays, AM technology uses competitive lasers and techniques for various applications, such as cutting, welding, and surface treatment, in schools for study and research and in small businesses. These techniques include conventional gas-assisted, remote, and non-conventional waterjet-guided laser cutting [16,30].
Regarding the competitiveness of these techniques, the advantages of laser cutting are, among others, the precision and flexibility of contour cutting, cutting and process speed, small heat-affected zone (HAZ), cut quality, and the ability of process automatization [5,31]. Figure 1 illustrates the process setup of conventional gas-assisted wood laser processing. with many applications [33]. This laser cutting technique has been considered to have numerous advantages over conventional laser cutting techniques. These advantages include active cooling of the workpiece and material ejection, high plasma pressure, quick debris removal, and tiny focal spot size resulting in lower burrs and burns [34]. Besides, the LMJ system can operate daily in the production environment. However, new laser technologies, such as disc and fiber lasers, have been successfully applied with unique demand to various applications in the past years. Since frequency-doubled Q-switched DPSS and disc lasers operating at 532 and 515 nm have become the traditional laser sources for most LMJ applications due to their excellent compatibility with the water absorption spectrum [32]. The laser wavelength is solely constrained by the water transmission spectrum compatibility, which is minimum in the optical spectrum's green region [35]. Notably, the absorption coefficient α in the waterjet is the lowest at a wavelength of 532 nm. At 1064 nm, the absorption coefficient is about 500 times higher. Light transmission over a 2.5 cm waterjet is as high as 99.9% at 532 nm and 60% at 1064 nm [32,35]. Hence, the light absorption at 532 nm can be neglected. Additionally, Nd: YAG laser sources with a wavelength of 1064 nm in pulsed or Q-switched regimes have also been used for water jetguided laser systems [22,26,27,32,36].

Principle
The concept of WJGL consists of coupling a pulsed laser beam with a thin, low-pressure water jet [37]. The basic principle includes guiding the laser beam into a nozzle passing through a pressurized water chamber. The pressured waterjet cooling from the nozzle conducts the laser beam with total reflection at the water/air interface until the workpiece. Once reaching the workpiece, the guided laser beam ablates the material via the melting-vaporization process.
Depending on the nozzle diameter, the water-filled chamber has a pressure range of 50-600 bars. Larger nozzle diameters require smaller water pressure. Hence, typical nozzle diameters range from 20 to 150 μm [32]. The waterjet acts as a stable fluid optically wave guided with different lengths. Besides, it owns two other primary functions, namely [37]: • The cooling of the workpiece cut surface, resulting in a negligible heat-affected zone (HAZ); • The removal of excesses, molten, or debris materials from the cut kerf (heat-material interaction zone); In other words, thin waterjet cooling prevents undesirable particles from being part of the surfaces, offering remarkable efficiency while minimizing contamination and thermal damage. Consequently, contamination and environmental risks are significantly reduced as the water jet develops high kinetic energy, efficiently removing the molten materials [32]. Furthermore, considering the small jet diameter and the low-pressured water, the waterjet's mechanical force is neglected. This force is much lower than that applied during gas-assisted laser cutting [32,37].

Hybrid WJG Nd: YAG laser wood micromachining
Similarly, to the gas-assisted laser process (Fig. 1), for a waterjet-guided laser, the waterjet guides the laser beam during the machining process. Hence, a pulsed Nd: YAG laser of 100-500 W can be assisted by a laminar water jet to cut different kinds of materials, such as ceramics, plastics, wood, and composites, with an extraordinary degree of quality and sizeable operating stand-off distance of up to 100 mm [16]. Applying waterjet-guided solid-state Nd: YAG laser systems in thin wood product prototyping is a novel development prospect. The water jet flows co/offaxially with a laser beam through an annular nozzle. This innovative cutting process also allows continuous beams where pulsed is required. For wood machining applications, experimental studies reported that water reduces the surface roughness, decreases the kerf width, increasing the cutting speed [23,26,38]. Figure 2 illustrates the hybrid waterjet-guided laser wood machining. The high energy density of the assisted laser beam is focused on the wood processing region. The lignin decomposition begins at approximately 280 °C [27]. As a result, the wood cell moisture evaporated quickly, resulting in an empty tracheid. Due to a rapid temperature change, a thermal stress gradient occurs around the cutting areas. Simultaneously, local expansion and contraction occurred, resulting in micro-cracks in the wood subtract and residual stress.
Regarding wood ignition temperature, the proceeded area's laser energy density is lower than vaporization's,  [23,27,[39][40][41]. Therefore, the waterjet attenuates HAZ expansion, the micro-cracks. Water-cooling affects the cut kerf, cleaning away excess heat and debris and improving the WGL wood micromachining efficiency accordingly. Figure 3 depicts the computer numerical control (CNC) WJG Nd: YAG laser system [26]. Here, wood is fixed on the workbench, and the laser moves all along the proceeded area via the feeding system. The water moves through the nozzle outlet onto the irradiated surface when the pump is switched on, forming a jet. Simultaneously, the laser beam from Nd: YAG laser system heats up, machining the wood workpiece. WJGL wood machining is a complex process involving multiphysics and thermal interactions. Thus, parameters of the laser system, waterjet equipment, and workpiece influence the process output. Figure 4 depicts a schematic illustration of these factors and sources based on Fig. 3.

Numerical relation of influencing process parameters
The waterjet mechanism is additional processing of the laser process, as illustrated in Fig. 2. Water is continuously sprayed around while the laser beam is heating the workpiece. Therefore, the moisture content in processed wood is ignored. The laser wavelength and pulse width are also fixed using a pulsed laser beam. Hence, the process factors for experimental WJGL wood machining include laser power and cutting speed, waterjet feed speed, water pressure, Nozzle outlet diameter, and wood thickness. For pulsed Nd: YAG laser thin wood machining, the cut depth D (mm) is assimilated to the wood material thickness, which is fixed during the processing [5,42]. As a result, laser beam energy has a remarkable influence on wood machining quality. Hence, assuming that all the absorbed laser energies melt/vaporize the wood workpiece while ignoring the heat convection and heat transfer loss, Eq. is used to express the relationship between laser power (P), cutting speed (V), and the cut kerf width (W) of processed wood material.
where Table 1 reports the detail of each variable in Eq. (1).
Since P i , V, W are concerned, one got an equivalent Eq. (3), deduced by considering the right-end of Eq. (2). P i is the incident laser power depending on the laser pulse energy E (m J) and pulse frequency f (Hz), expressed by Eq. (4) [5].
Using a pulsed Nd: YAG laser with pulse energy E from 10 to 800 m J and pulse frequency f from 1 to 15 Hz, the incident laser power P i is numerically from 0.01 to 12 W.
Since the wood workpiece thickness D and other auxiliary parameters remain fixed during the processing, Eq. Notably, the kerf width (W) is proportional to the incident laser power (P i ) and inversely proportional to the cutting speed (V) at constant β.

Cut surface geometry
The kerf geometry is one of the most factors characterizing the machining quality. Figure 5 illustrates the typical kerf geometry characterization of the laser cut surface of a solid material. In Fig. 5, W t , W b, and T a denote the top kerf width, bottom kerf width, and taper angle. The equation expresses the taper angle (T a ) function of W t , W b, and D [43].
where D (mm) denotes the proceeded solid material thickness.
Red pine wood and Ashwood types were selected for workpiece materials, namely Korean pine, and Northeast China ash. This selection considers the difference between the two wood materials' thermophysical properties and their significance for WJGL wood machining, taking them as references and guides for further wood manufacturing. Table 2 reports the fundamental physical characteristics of the purchased wood types (Haicheng Machining Factory, Harbin, China). The workpiece is prepared to have a specimen with a uniform thickness of 100 mm × 40 mm × 3 mm (length × width × height). Figure 6 shows the photography of the prepared samples of the two wood workpieces.

Equipment
A solid-state laser was selected depending on the wood laser-cutting mechanism, the thermophysical properties of proceeded material, and the test requirement vis-à-vis to the process parameters. Conventionally, wood laser cutting requires moderate laser energy. Therefore, due to its numerous advantages, versatility, and flexibility, an Nd: YAG (1064 nm) laser and auxiliary equipment ( Fig. 7) were used to build the WJG Nd: YAG laser system (Fig. 8). A laser generator machine has converted electric energy into light energy (Fig. 7b). For stable laser generating, the voltage fluctuation was about three percent (3%). The cooling system used an SK20P water-cooling machine of 600 W (Dongluyang Co., Ltd., Shenzhen, China) (Fig. 7c). Table 3 shows the performance parameters of the leading equipment of the WJG Nd: YAG laser system.

Experimental processes
Referring to Fig. 3, the mechanism with a three-axis linkage feeding plate was fixed to the optical platform. The beam adjustment was carried out before installing the laser system. Firstly, while turning on the infrared tuner, the mask of the entire mirror opened and pulled down. At this moment, the tuner's spot focused on the mask's center, adjusting its height. While opening the mirror mask, it is set behind the half mirror from the entire mirror and centered, obtaining a unique, fine-tuned, coherent beam's path. The mask is placed behind the focusing lens, fine-tuned, making the beam converge with the minimum diameter after passing through the entire mirror, half mirror, and solid-state laser. Once the beam is adjusted, Nd: YAG laser is mounted with the waterjet guided equipment  constituting the WJGL system, as shown in Fig. 8. The Gaussian (TEM00) laser beam had a 1 mm diameter and a pulse width of about 200 μs [5,22]. The focal length of the focusing lens was 150 mm, resulting in a focus depth of 61 mm and a focal spot size of about 0.02 cm. The workpiece is tested for an accurate operation, detecting water leakage. Depending on the waterjet cooling mechanism, an angle adjustment considers the adjustable annular nozzle to control the waterjet range for a non-overlapping with the laser beam, reducing heat loss and absorption in water. The nozzle inclination angle was adjustable to control the waterjet ring's range. The pressurized water of 0.13 MPa, flows from a nozzle outlet of 0.5 mm diameter with 5.75 m/s of waterjet speed [22,27]. The press roller placed in the return tank is used to fix the wood on the worktable surface. Since this workpiece is  motionless during the processing, its position must remain unchanged, facing the system's vibration. As a result, depending on machining conditions (Table 4), the WJG Nd: YAG wood machining is adopted. By gradually adjusting the (x, y, z) feeding system, a test is carried out using a single pass cutting method to verify the suitability of the equipment for further subsequent processing. The wood machining was conducted once the result met the standard test requirements. Thus, Korean pine and Northeast China ash wood specimen (Fig. 6) were machined under different machining conditions, as shown in Table 4.

Results and discussion
Based on a theoretical model expressing the relation between process parameters, influencing factors and effects on cut surface geometry have been analyzed. An experimental test was carried out using the WJG Nd: YAG system ( Fig. 8) to machine the red pine and ash wood ( Fig. 6) at constant parameters and material properties ( Table 2). As numerically expressed in Eq. (5), the control variable method was used to explore the relationship between the parameters. Firstly, the laser power was fixed constant while varying the cutting speed to cut the workpiece. Secondly, fixing the cutting speed, the laser power was adjusted to machine the wood workpieces as presented in Table 4. Five direct measurements of the cut kerf width were carried out using the mean value method for each selected value of laser power and cutting speed. Thus, the influence of laser power and cutting speed on cut kerf width, surface geometry, and quality are analyzed and discussed.

Micromorphology of Korean pine cut surface under machining conditions (M 2 )
Korean pine (Pinus Koraiensis) was laser cut at a constant cutting speed of 2.36 mm/s under different laser power of 2, 4, 6, 8, 10, and 12 W, pulse frequency of 15 Hz (M 2 ). As a result, Fig. 9 shows the machining parts and the corresponding surface micrographs of SEM. From Fig. 9, it is noticeable that the Korean pine (tube holes) lignin are approximately quadrilateral, arranged in longitudinal order. When the laser power is 4 W, the tube aperture is remarkably destroyed. The surface roughness is relatively high, presenting dross residues on the surface walls, challenging lignin visibility. At 6 W, the surface roughness is significantly improved with remarkable lignin structure, but with some remaining dross covering the tube hole. At 8 W, the cut surface is smooth, clean, visible tube aperture with no significant excess waste. Besides, the cutting quality is relatively excellent. However, when the laser  power is 10 W, the tube structure is destroyed, resulting in a rough surface with a significant dross presence on the cut surface. Table 5 reports the kerf width data of Korean pine at fixed cutting speed for different laser power (M 2 ). The graph of kerf width as a function of laser power is shown in Fig. 10. From Fig. 10, at a fixed cutting speed of 2.36 mm/s, the kerf width of the Korean pine increases linearly with the increase of the laser power, and the surface quality changes accordingly, as shown in Fig. 9. Notably, within a range of laser power, at 4 W and 12 W, respectively, for the minimum and maximum values, the surface quality of the kerf geometry is not quite good.

Kerf width variations of the two wood workpieces under conditions (M 2 )
Similarly, Northeast China ash's specimen was machined under the same conditions (M 2 ) with laser power as the single variable. The kerf width data is reported in Table 6. Figure 11 shows the graphical illustration of kerf width as a function of laser power. Figure 11 shows a remarkable variation of the Northeast China ash kerf width under different laser power, affecting the cut surface quality.    . Under different laser power, the kerf width rises gradually, and the curve (W = f (P)) slowly moves up. Consequently, the increase of the laser power leads to quick heat accumulation on the wood surface, resulting in a rapid rise in surface temperature. Under the laser beam's radiation, the wood-burning point is quickly reached. The temperature absorbed affects the kerf geometry and its surface quality accordingly.
Comparatively, under different laser power at fixed cutting speed, the kerf width variation of the Korean pine is slightly more significant than the Northeast China ash, as shown in Table 7 and Fig. 12, respectively, for kerf width data and corresponding joint graphs. This slight difference may depend on the physical properties of the two wood, as reported in Table 2. For instance, the Korean pine's air-dried wood density was lower than the Northeast China ash air-dry density. Besides, its physical properties inherent in laser energy absorption processing is quite different, resulting in the changes noticeable in Table 7.   Using the experimental data of the kerf width of the Korean pine and the Northeast China ash under condition M 2 as in appendix A [44], a One-Way ANOVA was carried out considering the WJGL power as the single independent variable. As a result, Table 8 describes the data statistics, while the ANOVA result is reported in Table 9. Table 10 shows the fit statistics of the data. The variance homogeneity was tested using Levine's (Absolute Deviations) test, as reported in Table 11.
From Table 9, in terms of the difference between the kerf width under laser power variation at a fixed cutting speed of 2.36 mm/s, the population means are significantly different at the α (0.05) level of variance. In other words, for Korean pine and Northeast China ash, there is a significant difference within the kerf widths at different laser power. Hence, laser power variation significantly influences the kerf width of the Pinus Koraiensis and Fraxinus mandshurica. Besides, the Tukey Test results of kerf width comparison of Korean and Northeast China ash using grouping the letter table is summarized in Table 12 (Appendix A [44]). The means that do not share a letter significantly differ at the 0.5 level. The value of Sigma (σ) was used to judge the comparison analysis. One can note that the means difference is significant at the 0.05 level of variance. Moreover, the population variance is significantly different (Table 11).

Influence of laser cutting speed on the cut
surface (kerf width, geometry, and surface roughness)

Micromorphology of Northeast China Ash (Fraxinus Mandshurica) cut surface under machining conditions (M 1 )
Fraxinus mandshurica specimen of 3 mm thick was machined under different laser cutting speeds of 1.57, 2.35, 3.62, 4.68, 5.34, and 6.26 mm/s, at a fixed laser power of 8 W. The micrographics images of SEM of the cut surface is shown in Fig. 13. From Fig. 13, the rounded with staggered lignin wood fiber structure is noticeable along the cut surface walls. At a cutting speed of 1.57 mm/s, the cut surface is extremely rough, presenting severe ring breakage of the tube aperture with trash and crimp at the cut kerf. When the cutting speed was 3.62 mm/s, the cut surface smoothness was improved with a faintly readable tube aperture and noticeable dross on the cut kerf. At a cutting speed of 4.68 mm/s, the cut surface is smoother, flat, and relatively excellent comparatively, clean and readable lignin structure with little dross presence. While, within a selected range, at the maximum cutting speed  of 6.26 mm /s, the cut surface smoothness decreased, with an abashed lignin structure. The kerf geometry and surface quality also decreased. The surface flatness felled accordingly; it is rough with slags on the cut kerf.

Kerf width variations under machining conditions (M 1 )
Under different cutting speeds as a single variable at a fixed laser power of 8 W, the kerf width data of the Korean pine and the corresponding variation illustration are presented in Table 13 and Fig. 14, respectively. For Northeast China ash, the kerf width data are reported in Table 14. Figure 16 illustrates the specific variation trend.
In Figs. 14 and 15, one notices that the cutting speed variation influences remarkably the kerf widths of both types of wood specimens. For a selected wood workpiece of 3 mm thick under M 1 , the increase of the WJGL cutting speed entrained the kerf width decrease, directly affecting the kerf geometry and cut surface quality accordingly, as shown in Fig. 13. Consequently, the laser beam interaction  with the wood is quite long at a low cutting speed. As a result, the heat accumulation time is extended, resulting in broader kerf width with a sizeable heat-affected zone (HAZ). Contrariwise, when the cutting speed increases, the interaction time is shortened. The wood-burning speed is lower than the cutting speed, resulting in a gradual decrease of the cut depth and the kerf width accordingly. However, within a range of cutting speed, at maximum cutting speed, the kerf width is thinner with dotted, serrated, little rough kerf geometry and surface (Fig. 13). Similarly, as in M 2 , under machining conditions M 1 , there is a slight difference between the kerf width data of the two wood. The kerf width variation of Korean pine was still slightly more significant than the kerf width variation of Northeast China ash like in M 2 , as noticed in Table 15 and graphically illustrated in Fig. 16.

• Analysis of variance (ANOVA)
Under M 1 , using kerf width data of the Korean pine and Northeast China ash wood (Appendix A [44]), a One-Way ANOVA with a single independent variable of WJGL cutting speed was carried out. As a result, Table 16 shows the data statistics, and Table 17 presents the overall ANOVA summary. Table 18 reports the Fit statistics of the data. The variance homogeneity tested using Levine's test (Absolute Deviations) is reported in Table 19.
Considering the kerf widths of Korean pine and Northeast China ash under M 1 , as shown in Table 17, the population means are significantly different at the α (0.05) level of variance. In addition, the population variances are different (Table 19). In other words, there was a significant difference within the kerf widths at different laser cutting speeds. Consequently, cutting speed affects the kerf width of the Korean pine and Northeast China ash. Furthermore, the kerf width comparison of the two workpieces using the Tukey Test (Appendix A [44]) summarized by the grouping letter table is reported in Table 20. The means that do not  share a letter are significantly different at the 0.05 level of variance. One can note that at the 0.05 level of variance, the means difference between the Korean pine and Northeast China ash under machining conditions (M 1 ) is slightly significant.

Influence of the WJG laser power and cutting speed on the wood kerf width under M 1 and M 2
A two-way ANOVA with replication was conducted using Korean pine and Northeast china ash (Table 21) under M 1 and M 2 ( Table 2). The data repartition in the histogram is illustrated in Fig. 17.

Effects on the kerf width of Korean pine (Pinus Koraiensis)
Under M 1 and M 2 , a two-way ANOVA with laser power and cutting speed as independent variables influencing the Korean pine's kerf width was reported in (Appendix B [44]). The data statistic is summarized in Tables 22, Table 23, and  Table 24, respectively, for laser cutting speed, laser power, and interactions. Table 25 shows the overall ANOVA result. The kerf width comparison was evaluated using Bonferroni Test (Appendix B [44]). The value of Sigma (σ) judges the comparison analysis. Thus, Sig equals one (σ = 1) indicates that at a 0.05 level of variance, the difference of the means is significant, whereas Sig equals zero (σ = 0) shows that the difference is not significant. The grouping letter table of the Bonferroni Test summarizing the mean's comparison is reported in Table 26 and  Table 27, respectively, for the cutting speed, the laser    level of variance, the two-way ANOVA concluded as follows: • The population means of Cutting speed are not significantly different. • The population means of Laser power are significantly different. • The interaction between Cutting speed and Laser power is significant.

Effects on the kerf width of Northeast China ash (Fraxinus Mandshurica)
Considering the kerf width data of Fraxinus mandshurica under different values of laser powers and cutting speed ( M 1 and M 2 ) (Appendix C [44]), the two-way ANOVA is statistically reported in Tables 28, 29, and 30 for laser cutting speed, power, and interaction, respectively. Table 31 reports the overall ANOVA results. The kerf width comparison was also evaluated using Bonferroni Test, as reported in (Appendix C [44]). The grouping letter table summarizing the Bonferroni Test is reported in Tables 32 and 33 for the cutting speed, laser power, and     Figure 19 illustrates the graphical representation of the kerf width of Northeast China ash wood workpiece under machining conditions M 1 and M 2 .
Regarding the effects of the laser power and cutting speed on the Northeast China ash kerf width at 0.05 level of variance under M 1 and M 2 : • The population means of Cutting speed are significantly different. • The population means of Laser power are significantly different. • The interaction between Cutting speed and Laser power is not significant.
WJG Nd: YAG laser is suitable and efficient for wood machining, including softwood and hardwood. The technique provides outstanding machining results, plus it is flexible, safe, and eco-friendly [23,26,27]. Moreover, the waterjet reduced the surface roughness in addition to the cooling and cleaning functions; it decreased the kerf width by increasing the cutting speed due to water vaporization creating additional kinetic energy in the cutting region [23,26,38]. WJG Nd: YAG cutting is a suitable technique for wood machining, including thin wood from soft and hardwood. However, this hybrid WJGL processing involves multiphysics phenomena that affect irradiated surface temperature and influence machining quality. These phenomena include interaction between laser, pressurized waterjet, and air on the processed workpiece surface, which was ignored in the present study. Therefore, for further efficient and outstanding WJG Nd: YAG laser wood machining, additional studies are needed to consider the above concerns and better understand the temperature distribution (heat transfer) within the workpiece during the machining.

Conclusion
In this practical application of waterjet-guided Nd: YAG laser machining, the effect of influencing process parameters on cut geometry, surface, and kerf width were experimentally analyzed using the Korean pine and Northeast China ash. Based on the numerical relationship between the cut kerf width and the machining parameters, and through experimental results and analysis, the following conclusions are drawn: 1. At constant cutting speed and fixed workpiece thickness, the machining surface quality of the kerf geometry improved gradually with the increase of laser power. Excellent surface quality was obtained at the laser power of 8 W. However, with the growth of laser power, wood lignin laser beam's damage increases, decreasing the cut surface quality. Comparatively, the kerf width variation of the Korean pine was slightly more significant than the Northeast China ash.